Name: ____________________________________ Date: _________________ OTHER TYPES OF REGRESSION COMMON CORE ALGEBRA I In the last two lessons we fit bivariate data sets with lines of best fit. Sometimes, though, linear models are not the best choice. We can fit data with all sorts of curves, the most common of which are linear, exponential, and quadratic. But, there are many other types. Before we look at exponential and quadratic regression, recall the general shapes of these two types of functions. EXPONENTIAL AND QUADRATIC GRAPHS EXPONENTIAL GRAPHS QUADRATIC GRAPHS Exercise #1: For each scatterplot shown below, determine if it is best fit with a linear, exponential, or quadratic function. Draw a curve of best fit depending on your choice. (a) (b) (c) Type: ________________ Type: ________________ Type: _______________ Type: _________________ Type: ________________ Type: _______________ (d) COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013 Our calculators can produce equations for exponentials of best fit and quadratics of best fit (along with a lot of other types of curves). Exercise #2: Biologists are modeling the spread of flu cases as the spread around a particular city. The total number of cases, y, was recorded each day, x, after the total first reached 16. The data for the first week is shown in the table below. x, days 0 1 3 64 6 7 y, cases 16 (a) Use your calculator to find the exponential regression equation for this data set in the form y a b x 18 22 25 33 35 (b) Based on the regression equation, how many total cases of flu will there be after two weeks? Round all parameters to the nearest hundredth. (c) According to your model, by what percent are the flu cases increases on a daily basis? (d) Hospital officials will declare an emergency when the total number of cases exceeds 200. On what day will they need to declare this emergency? So, really, regression, as mysterious as it may be, is all about finding the best version of whatever curve we think fits the data best. Exercise #3: The cost per widget produced by a factory generally drops as more are produced but then starts to rise again due to overtime costs and wear on the equipment. Quality control engineers recorded data on the cost per widget compared to the number of widgets produced. Their data is shown below. Number of widgets, x 35 88 110 135 154 190 Cost per widget, y 9.32 2.63 1.42 1.32 2.12 5.50 (a) Why should a quadratic model be considered for this data set as opposed to linear or exponential? (b) Use your calculator to create a scatterplot of this data to verify its quadratic nature. COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013 Name: ____________________________________ Date: _________________ OTHER TYPES OF REGRESSION COMMON CORE ALGEBRA I HOMEWORK FLUENCY 1. For each scatterplot below, determine the best type of regression from: linear, exponential, or quadratic. Draw a representative curve (line, exponential, or parabola) through the data. (a) (b) Type: ________________ (d) (c) Type:__________________ (e) Type: _______________ Type: _______________ (f) Type: ________________ Type: _______________ 2. Given the scatterplot below, which of the following equations would best mode the data? Explain your choice. (1) y 3x 6 (3) y 4 x2 20 x 3 (2) y 6 2 (4) y 2 x 2 6 x 4 x COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013 APPLICATIONS 3. A marketing company is keeping track of the number of hits that a website receives on a daily basis. Their data for the first two weeks is shown below. A scatterplot of the data is also shown. Hits 0 120 3 145 5 162 10 220 14 270 Daily Hit Count for Site 300 Days 200 100 (a) Of the three types of regression we have studied which seems least likely to fit this data? Explain your choice. 5 10 15 Days After the Website Launched (b) Find a linear equation, in the form y ax b , that best models this data and an exponential equation, in the form y a b that best models this data. Round all parameters to the nearest hundredth. x Linear Model Exponential Model (c) How close are the two model’s outputs when x 10 ? Show the values you find. (d) How close are the two model’s outputs when x 30 ? Show the values that you find. (e) Which model will predict faster growth of website hits over time? Explain your answer. You may want to experiment by graphing both models. COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013

1/--pages